Symmetry axes of planar polynomial differential systems

The notion of $N$-type axis of symmetry is introduced. It is proved that the vector field defined by system of the differential equations with $n$-order polynomials in a right hand, cannot have even number of axes of symmetry $N$-type at $n=2m$, $m\in N$. For $n=2,3$ full research of the given system on $N$-symmetry is carried out. Depending on the number of axes of $N$-type symmetry special forms of presenting of square and cubic systems,which allowto simplify qualitative research of such systems, are discovered.